In 1981 the CAB was given the authority to give domestic fill-up rights on international flights. For example, an international carrier flying from LAX to Rome via JFK could be given the authority, even though not previously possessed, to carry domestic traffic between LAX and JFK on at least one round-trip flight a day. (Wells, Alexander. Air Transportation. 1998)

The CAB ceased in 1985, but this provision was given to the DOT (among many other provisions).

Was any exemptions ever given (or applied for by a foreign carrier)?

When was this provision repealed?

If this was not repealed by the DOT between 1985-today, could an international air carrier apply for a grant to fly domestic traffic between US cities?

The Bahamas allows US-carrier Chalk's Ocean Airways to carrier domestic passengers. In addition, for a small time in late 2001, Australia allowed United to fly domestic passengers in Australia on MEL-SYD.